6 - The Sutras of Vedic Mathematics



Vedic Mathematics is becoming increasingly popular as more and more people
are introduced to the beautifully unified and easy Vedic methods.
The purpose of this Newsletter is to provide information about developments
in education and research and books, articles, courses, talks etc., and also
to bring together those working with Vedic Mathematics.
If you are working with Vedic Mathematics- teaching it or doing research-
please contact us and let us include you and some description of your work in
the Newsletter. Perhaps you would like to submit an article for inclusion in
a later issue.

If you are learning Vedic Maths, let us know how you are getting on and what
you think of this system.


This issue's article:

The Sutras of Vedic Mathematics

Sri Bharati Krsna Tirthaji who reconstructed the system of Vedic Mathematics
between 1911 and 1918 tells us that Vedic Mathematics uses sixteen Sutras and
some sub-Sutras. There is no doubt that this mathematical system is extremely
powerful and coherent, but there are a number of questions that arise about
the Sutras themselves. These include questions about the origin of the
Sutras, their structure, their comprehensiveness and their relation to the

We do not know, for example, where the Sutras come from. Are they from one of
the countless Vedic manuscripts as Bharati Krsna implies, or did he discover
them for himself? The word 'Veda' means 'Knowledge' and also refers to a vast
number of Sanskrit texts in India known as the Vedas. Bharati Krsna tells us
that he found some clues in certain texts and gradually rediscovered the lost
Vedic system. The best explanation for the origin of the Sutras is therefore
that Bharati Krsna cognised them or some of them himself. And this fits
perfectly with the first meaning of the word Veda, that of pure knowledge.

Close examination of these Sutras suggests that though they are given in
mathematical form they refer to fundamental principles which go beyond what
we normally think of as mathematics. It is therefore possible to relate the
Sutras (and sub-Sutras) to functions of mind: each Sutra and sub-Sutra
describing a commonly used type of mental activity. The Sutra 'By One More
than the One Before' relates to the processes of deduction and implication
where one idea follows from another, and 'Transpose and Apply' refers to the
reversal technique that we often find useful in our thinking. We cannot go
into greater detail here but many of the questions relating to the Sutras and
sub-Sutras can be answered by looking at the Sutras from this standpoint.

This also adds an extra dimension to the use of the Sutras as an educational
tool. Not only do they have mathematical applications but they also offer the
student a way to go about solving problems. In first looking at a question
the student may not know what to do - how to begin to think about the
problem. There seem to be very many possibilities, many ways of using the
mind, and the Sutra indicates a starting point. The rest of the method then
follows on. A motorist on a narrow country lane encountered a flock of sheep
being driven along by a shepherd. After some time the motorist was getting
very impatient. The shepherd stopped his flock and quietly drove the sheep
back past the car. The motorist then drove off and the shepherd continued on
his way. This is an example of using reversal (Transpose and Apply) to solve
a problem. It is getting started that the student often finds difficult.
Since mathematics is perceived in the mind, the validity of the Sutras as a
basis for mathematics could be established once it is demonstrated that there
are sixteen basic mental activities and that these correlate with the sixteen



#1. There will be an introductory lecture on Vedic Mathematics given by James
Glover, head of mathematics at St James School, London, on Tuesday 29th
February. This will be at University College London, Computing Department at
5.30 p.m. This talk follows one James Glover gave on 17th February at
Imperial College as a guest of the Hindu Society. The talk, which was
attended by about 50 students, lecturers and guests, gave a brief history and
description of Vedic Mathematics with audience participation on recurring
decimals. It also touched on some aspects of coordinate geometry, the
binomial theorem and calculus. All seemed extremely impressed, particularly
the computer boffins and those who thought maths difficult. The main question
people asked was "Why is this not more widely known about?" Mr Glover has
been invited to give a series of talks/workshops in the Autumn at the same
venue. We will keep you informed.

#2. A talk has been organised by Howard Chester, Inspector of Maths and
Primary Education, for Richmond Upon Thames. This is entitled "An Oral
Tradition in Geometry" and is given by Andrew Nicholas on Wednesday 8th
March, 4.15 - 5.45 p.m. This is at Richmond Curriculum and Teachers' Centre,
Clifden Road, Twickenham, Near London. This is an exciting approach to
geometry which could have implications for teaching. Particularly in the
areas of oral and mental strategies, extension work with higher attaining
pupils and multicultural mathematics. There will be an opportunity to discuss
the approach and look at ways in which it might be used in the classroom.
This course will be of interest to both primary and secondary teachers.
Entrance free.

#3. James Glover's Book 2 of "Vedic Mathematics for Schools" is now published
and available.

#4. An article on Vedic Mathematics by Andrew Stewart-Brown is due to appear
in "Mathematics Teaching" No. 170, March issue. This is a publication of the
Association of Teachers of mathematics.

#5. There has been a review of the little book "Fun with Figures" by Kenneth
Williams. It is from 'inTouch', Jan/Feb 2000, the Irish National Teachers
Organisation (INTO) magazine.
"Entertaining, engaging and eminently 'doable', Williams' pocket volume
reveals many fascinating and useful applications of the ancient Eastern
system of Vedic Maths. Tackling many number operations encountered between
First and Sixth class, Fun with Figures offers several speedy and simple
means of solving or double-checking class activities. Focusing throughout on
skills associated with mental mathematics, the author wisely places them
within practical life-related contexts."
"Compact, cheerful and liberally interspersed with amusing anecdotes and
aphorisms from the world of maths, Williams' book will help neutralise the
'menace' sometimes associated with maths. It's practicality, clear
methodology, examples, supplementary exercises and answers may particularly
benefit and empower the weaker student."
"Certainly a valuable investment for parents and teachers of children aged 7
to 12."
(Reviewed by Gerard Lennon, Principal, Ardpatrick NS, Co Limerick.)

#6. The Vedic Square. If you take a 10 by 10 square and put the numbers from
the 1 times table in the first row, the 2 times table in the second row, and
so on up to the 10 times table, and if you then replace the number in every
square by its digit sum (you add the number's digits until you have a single
figure) you will have a Vedic Square. This square has many interesting
properties. Shreepad Hardas has sparked enquiries into the origins of this
square. If you know anything about this (or if you would like to mention an
application or property of this square) please let us know.

#7. Our web site (www.vedicmaths.org) continues to be updated and improved
due to the continued efforts of Mr Clive Middleton. Thank you Clive. The
first chapter of "The Circle Revelation" can now be viewed on the site.

#8. The Centre for Vedic Mathematics in Singapore has changed. The new name,
address and telephone numbers are:

Vedic Mathematics Education Svcs
113 Tai Keng Gardens
Singapore 535394
Tel : +65 8580414
Fax : +65 8583224
Email :
Person to Contact : Raaj (Mr), Project Co-ordinator
Pager No : +65 92591720


Your comments about this Newsletter are invited.
If you would like to send us details about your work or submit an article for
inclusion please let us know on

Articles in previous issues of this Newsletter can be copied from the web
site - www.vedicmaths.org:
Issue 1: An Introduction
Issue 2: "So What's so Special about Vedic Mathematics?"
Issue 3: Sri Bharati Krsna Tirthaji: More than a Mathematical Genius
Issue 4: The Vedic Numerical Code
Issue 5: "Mathematics of the Millennium"- Seminar in Singapore

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27th February 2000


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